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Ponderomotive effects in the femtosecond
plasmon-assisted photoelectric effect in bulk metals:
Evidence for coupling between surface and interface
plasmons
Michèle Raynaud, Joseph Kupersztych
To cite this version:
Michèle Raynaud, Joseph Kupersztych. Ponderomotive effects in the femtosecond plasmon-assisted
photoelectric effect in bulk metals: Evidence for coupling between surface and interface plasmons.
Physical Review B: Condensed Matter and Materials Physics (1998-2015), American Physical Society,
2007, �10.1103/PhysRevB.76.241402�. �hal-01327436�
Ponderomotive effects in the femtosecond plasmon-assisted photoelectric effect in bulk metals:
Evidence for coupling between surface and interface plasmons
Michèle Raynaud
*
and Joseph KupersztychSPCSI, CEA/Saclay, 91191 Gif-sur-Yvette, France
共Received 18 October 2007; published 12 December 2007兲
The existence of ponderomotive acceleration effects in the metal bulk has been experimentally demonstrated in the context of the femtosecond plasmon-assisted multiphoton photoelectric effect in metal systems. The resulting electron energy spectra show that these effects essentially depend on the coupling between the surface and interface plasmons. While the essential part played by the ponderomotive force of the surface plasmon is to accelerate the photoelectrons in the vacuum, the dramatic enhancement of the photoelectron production and the angular dependence in the photoemission process mainly result from ponderomotive effects in the metal bulk.
DOI:10.1103/PhysRevB.76.241402 PACS number共s兲: 78.70.⫺g, 73.20.Mf, 78.40.Kc, 79.60.⫺i
In the photoelectric effect in metals, photoelectrons may be emitted from a region near the metal surface1,2 or may
originate from the bulk.3 In the bulk, electron excitation
oc-curs via photon absorption in the presence of a third body 共ion or impurity兲 or through interband transitions. On the other hand, the surface effects play an essential role for the number of electrons emitted while the absorption of light energy in the surface layer共a few nanometers兲 is relatively small 共about 0.1% of the total absorption rate兲. In recent years, much attention has been paid to the possibility of en-hancing electron emission of metals through the surface pho-toelectric effect by means of light excitation of electron col-lective oscillation modes localized near the metal surface.4
Recently, it has been shown that the photoelectrons emerging from a metal via a multiphoton photoelectric effect in the presence of femtosecond laser-excited surface plasmons are much more energetic than in conventional photoemission.5–9
The phenomenon has been interpreted in terms of pondero-motive acceleration of the photoelectrons in the vacuum by the strongly inhomogeneous high-frequency electric field of the surface plasmon surrounding the metal surface.5
However, ponderomotive effects are not restricted to those electrons that have been released out of the metal. The field of the surface plasmon is also strongly inhomogeneous in the metal due to its small spatial extension. For example, by using a simple dielectric description,10the valueD of the depth at which the field amplitude of the surface plasmon falls to 1/e, for a metal like gold and for a laser wavelength of 800 nm, is readily obtained asDM⯝22 nm in the metal
andDV⯝650 nm in the vacuum. The ponderomotive force
Fp⯝Up/D 共where Up denotes the ponderomotive potential
of the surface plasmon兲 is thus 30 times stronger in the metal than in the vacuum. In this paper, we will show that, under certain conditions, inner-metal ponderomotive acceleration effects exist and that they can play an essential part in the photoemission process in the presence of resonant electron collective excitations.
To this end, let us consider a bilayer metal structure such as a thin gold overlayer of thicknessL deposited on a mas-sive aluminum sample, the surface of which is periodically structured to form a grating surface. For an optimum over-layer thickness Lopt, the field of the laser-excited surface
plasmon can tunnel through the overlayer and excites elec-tron density fluctuations共interface plasmons兲 at the interface between the two metals.11Arguing by analogy with the
phe-nomenon of ponderomotive acceleration of the electron in vacuum by the field of the surface plasmon, ponderomotive acceleration of the conduction electrons by the strongly in-homogeneous field of the interface plasmon can occur, so that energy and momentum can be transferred from the in-terface plasmon to the electrons in the bulk of the overlayer. The existence of such a phenomenon was invoked to explain the reduction of the number N of photons needed to be ab-sorbed by each photoelectron in the multiphoton photoelec-tric process and the corresponding increasing of the photo-emission probability by a factor greater than 104 in comparison with a homogeneous metal structure.12
It should be remarked that the energy transfer from the surface plasmon to the electrons in the metal bulk is a mechanism that manifests itself through significant modifi-cations in the photoemission process itself. As some part of the electromagnetic energy of the surface plasmon is pumped by the field of the interface plasmon to drive electron density fluctuations at the metal-metal interface, the magnitude of the interface plasmon is expected to increase at the expense of a depletion of the surface plasmon amplitude. As a con-sequence, the ponderomotive force experienced by the pho-toelectrons in the evanescence length of the surface plasmon will decrease, so that their kinetic energy will decrease ac-cordingly. Therefore, experimental evidence for the coupling between surface and interface plasmons can be obtained by comparing the electron energy spectra resulting from differ-ent metal structures, depending on whether the conditions for interface plasmon excitation exist or not.
In order to investigate the part played by inner-metal pon-deromotive acceleration effects, we have performed a sys-tematic study of the electron energy spectra together with the angular variations of the photoemission. We used a magneti-cally shielded time-of-flight spectrometer of length 60 cm. The surfaces of the targets were located at 0.7 cm from the spectrometer, the acceptance angle of which was smaller than 2°. The energy resolution was less than 0.1 eV for a flight potential of 2 V. For these values and in the range of the detected photoelectron signals, space charge effects were
verified to be negligible. The principle of these experiments is schematically described on Fig.1.
To determine the optimum conditions for the mechanism of energy transfer to the conduction electrons, we first per-formed angle-integrated experiments similar to those previ-ously described12on a series of metal gratings made of gold
overlayers with thicknessesL from 18 to 200 nm deposited on a massive aluminum sample. The wavelength of the
p-polarized laser beam was 800 nm, so that four photons of
energy 1.55 eV need to be absorbed per electron, as required by the multiphoton photoelectric equation 共polycrystalline gold work function WAu= 5.1 eV兲. The optimum electron sig-nal was still obtained with a sample with gold overlayer of thickness near Lopt⯝43 nm for the resonance angle res = 67°. For this optimum thickness, as was already shown in Ref.12, the number of absorbed photons per electron in the photoemission process, characterized by the variations of the photoelectron current versus laser intensity, for intensities as low as I = 0.1 GW/cm2, was 3 instead of 4. In fact, this result reveals that the conduction electrons in the metal overlayer have gained some additional energy due to the presence of the electron collective excitation, so that they need to absorb a lower number of photons to overcome the potential barrier at the metal surface. Hence, in keeping with the above dis-cussion, this effect is expected to be accompanied by a si-multaneous decrease of the photoelectron energy due to the corresponding depletion of the surface plasmon energy. In other words, for equal laser intensities and pulse durations, the energy of the photoelectrons is expected to be lower in the case of the optimum bilayer emissive sample than in the case of the ultrathick gold sample, where interface plasmon excitation cannot occur.
The electron energy spectra shown in Fig. 2 are quite significant inasmuch as they reveal, as expected, that the photoelectrons emitted by the most emissive sample 共Lopt ⯝43 nm兲 are much less energetic than those produced by the least emissive共bulk兲 gold sample 共L=200 nm兲 and the thin-ner bilayer sample共L=28 nm兲. Hence, for equal laser inten-sities, the ponderomotive force of the surface plasmon is effectively weaker in the case of the optimum emissive bi-metal sample than in the case of the bulk gold sample, where an interface plasmon cannot exist. This result clearly shows
evidence for the coupling between the surface and interface plasmons.
Furthermore, another piece of evidence for this coupling has been obtained by investigating the electron response of the various bilayer samples at different laser intensities. As a matter of fact, when the surface plasmon is coupled to the field of the interface plasmon, as is the case for the most emissive sample, its energy is optimally transferred to the interface plasmon and, because of this dissipation of the sur-face plasmon energy, the dependence of the photoelectron energy on the laser intensity is no longer linear. Thus, a nonlinear electron response of the bilayer samples can be evidenced by measuring the electron energy spectra at differ-ent laser intensities. In Fig.3, the spectra obtained by simply doubling the value of the laser intensity are represented. It clearly appears that the position of the peaks corresponding to gold overlayer thicknesses of 28 and 43 nm does not vary linearly, with the laser intensity, in contrast with the peak corresponding to an overlayer thickness of 200 nm. It can therefore be concluded that the electron response is not linear when interface plasmon excitation can occur and is linear when only a surface plasmon is excited.
FIG. 1. Schematic representation of the angular detection of the photoelectrons. The target can be moved to vary the incidence angle of the laser and so that the normal nជ to the surface lies within the
detection angle of the spectrometer. typical samples with gold overlayer thicknesses 200FIG. 2. 共Color online兲 Photoelectron energy spectra for three共䊏兲, 28 共䉱兲, and 43 nm共•兲. The laser intensity was I=4 GW/cm2and the pulse
duration 200 fs.
FIG. 3. 共Color online兲 Same as in Fig. 2 but for
I = 8 GW/cm2.
MICHÈLE RAYNAUD AND JOSEPH KUPERSZTYCH PHYSICAL REVIEW B 76, 241402共R兲 共2007兲
An estimate of the maximum energy ⌬E that can be gained by the conduction electrons through ponderomotive acceleration can be obtained as follows. The final kinetic energyE of a freed electron of initial kinetic energy Eiin a
high-frequency plasmon field共in the case of full conversion of the ponderomotive potential13兲 can be easily obtained as
E共兲 = Up+ 2Up关共Ei/2Up兲1/2− cos兴2, 共1兲
where Up= e22E02/4m02 denotes the ponderomotive poten-tial of the plasmon, E0 is the amplitude of the laser field of angular frequency 0, 共兲 is the resonance factor for an effective plasmon lifetime, andis the phase seen by the electron at the instant of its release. The final energy of the photoelectron thus depends both on the value of the pondero-motive potential and on the initial phase experienced by the freed electron.5,13In particular, the main peak in the electron
energy spectrum provides the value of the ponderomotive potential of the surface plasmon via the simple relation
具E典= 2Usp共1 + Ei/2Usp兲, 共2兲
while its broadening results from the random phase of the plasmon field experienced by the released electrons. An im-mediate consequence shown by Eq.共2兲 is that, in the
reso-nant case共UspⰇEi兲, the value of the main electron energy
peak varies linearly with the ponderomotive potential of the surface plasmon, that is, the laser intensity, a property that is exemplified in Figs.2and3through the electron response of the ultrathick gold sample. The value of the ponderomotive potential Uspof the surface plasmon, for a given laser
inten-sity, can thus be obtained from Eq.共2兲 and from the
mea-sured values of the energy of the photoelectrons emitted by the target. On the other hand, if␣denotes the fraction of the surface plasmon energy transferred to the interface plasmon via the tunneling effect, conservation of energy can be ex-pressed as
共DM+DV兲␣Usp⯝ 2DMUip, 共3兲
where Uipdenotes the ponderomotive potential of the
inter-face plasmon. The order of magnitude of the maximum en-ergy ⌬E that can be gained by the conduction electrons is then readily obtained via Eqs.共2兲 and 共3兲. For example, for a
laser intensity I = 8 GW/cm2, Fig. 3 gives U
sp共8兲⯝23 eV.
Thus, for the same ultrathick gold sample, using the above linearity property, the value of the ponderomotive potential of the surface plasmon for a laser intensity I = 0.1 GW/cm2is
Usp共0.1兲⯝0.28 eV. It follows that, with DM⯝22 nm and
DV⯝650 nm, the value of the ponderomotive potential of
the interface plasmon is, in eV, approximately Uip共0.1兲
⯝4.3␣, and the maximum energy that can be acquired by the conduction electrons is then given by Eq.共2兲 with
pondero-motive potential Uip as ⌬E共0.1兲⯝8.6␣. Hence, for a laser
intensity near I = 0.1 GW/cm2, it appears that only three pho-tons of energy 1.55 eV instead of four need to be absorbed by the energetic conduction electrons to overcome the gold work function WAu= 5.1 eV, as shown in Fig. 3 of Ref. 12, provided the fraction of energy transferred from the surface plasmon to the interface plasmon is at least of the order of 5%. This phenomenon is likely to occur for the sample with an optimum overlayer thickness 共Lopt⯝43 nm兲. For less emissive samples, such as thinner bilayer samples of thick-nessL=28 or 18 nm, the coupling parameter␣is smaller, so that the corresponding changes of slope12require higher
val-ues of the ponderomotive potential, that is, higher laser in-tensities.
On the other hand, it is worth noting that ponderomotive effects in the metal bulk play also an essential part in the angular dependence of the photoemission process in the presence of electron collective excitation. As the fields of the surface and interface plasmons are essentially directed along the normal to the metal surface, the corresponding pondero-motive forces, which are also directed along the normal to the surface, tend to deviate the electrons in the same direc-tion. Hence, the photoelectrons that would be mainly emitted
FIG. 4. 共Color online兲 Plasmon resonance angles for three samples of overlayer thicknesses: 200 nm 共䊏兲, 43 nm 共•兲, and 28 nm 共䉱兲. The laser intensities were, respectively, 1, 0.1, and 0.15 GW/cm2, and the pulse durations 50 fs.
FIG. 5.共Color online兲 Photoelectron energy spectra produced by the most emissive sample 共overlayer thickness 43 nm兲 for three laser incidence angles: =res= 67° 共䉱兲, =69° 共•兲, and =74°
共䊏兲. The laser intensity was I=4 GW/cm2and the pulse duration
along the direction of polarization of the laser field in the absence of electron collective excitation are deviated toward the normal to the metal surface via a ponderomotive accel-eration effect and are not collected in the spectrometer. This explains why, in apparent contradiction with the angle-integrated measurements, the electron current emitted by the most emissive sample is much lower共see Figs.2and3兲 than
those given by the samples of overlayer thicknessesL=200 and 28 nm.
To more precisely explore the angular dependence of the photoemission, we have employed a method that takes ad-vantage of the broadening共due to the coupling between the two opposite faces of the overlayer兲 of the surface plasmon resonance angle of the bilayer metal samples共see Fig.4兲. By
simply rotating the metal sample共see Fig.1兲, we could
eas-ily vary the incidence angle of the laser beam within the broadening range, keeping in mind the fact that the magni-tude of the surface plasmon decreases correspondingly. The resulting energy spectra displayed in Fig. 5 show, as ex-pected, that the more the incidence angle of the laser differs from the optimum plasmon resonance angle共res= 67°兲, the more the energy of the photoelectrons is reduced due to the decrease of the ponderomotive force in the vacuum. On the other hand, when the angle of incidence is close to the value
⬜= 74°, for which the perpendicular to the metal surface just coincides with the axis of the spectrometer, the detected photoelectron signal becomes maximum. We can therefore conclude that the photoelectrons resulting from the most emissive sample are essentially emitted perpendicularly to the metal surface and that this angular dependence is mainly due to a ponderomotive effect in the metal bulk.
In conclusion, enhanced photoemission in the presence of laser-excited surface and interface plasmons can be inter-preted as a Spicer-like three-step process.3 In the first step,
the electrons in the metal bulk are accelerated toward the surface by the ponderomotive force of the interface plasmon. The second process is a quantum absorption phenomenon in which the energetic conduction electrons absorb a number of photons lower than the minimum number required by the multiphoton photoelectric equation to overcome the work function of the metal.12 Finally, the released electrons can
gain a large amount of energy because of their acceleration in the vacuum by the ponderomotive force of the surface plasmon.5–8
We gratefully acknowledge the technical staff of the LUCA Saclay Laser Facility for their help in the experi-ments.
*Present address: LSI, CEA/Saclay, 91191 Gif-sur-Yvette, France.
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MICHÈLE RAYNAUD AND JOSEPH KUPERSZTYCH PHYSICAL REVIEW B 76, 241402共R兲 共2007兲
